Partial Diversion of a Stream through a Slot

Consider an inviscid uniform fluid flowing with velocity (expressed in ) parallel to a wall. A narrow slot in the wall allows some of the fluid to be diverted. The volumetric flow rate of withdrawn fluid is (expressed in ).

The Demonstration plots the stream function for this partial diversion problem, which is given by:

.

For small values of or large values of , the velocity profiles approach that of a uniform flow. Far from the slot, the velocity field is again almost that of uniform flow parallel to the wall.